What is the $x$-intercept of the line perpendicular to the line defined by $3x-2y = 6$ and whose $y$-intercept is 2?
Explanation: By subtracting $3x$ and dividing both sides by $-2$ we get $y = \frac 32 x - 3$ meaning this line has slope $\frac{3}{2}$ and any line perpendicular to it has slope $-\frac{2}{3}$.  Using the slope-intercept form of a line we get that the equation of the line perpendicular to it with $y$-intercept of 2 is $y = -\frac{2}{3} x + 2$.  We find the $x$-intercept by letting $y = 0$ which gives $x = \boxed{3}$.